Abstract : Controller Area Network (CAN) is widely used in automotive applications. With CAN, the network utilisation that may be obtained while ensuring that all messages meet their deadlines is strongly dependent on the policy used for priority (message identifier) assignment. This paper addresses the problem of priority assignment when some message identifiers are fixed. There are two variants of this problem: P1 where the gaps between fixed identifiers are large enough to accommodate the freely assignable messages and P2 when the gaps are too small. For problem P1, we provide algorithms that give optimal and robust priority orderings based on an adaptation of existing techniques. Problem P2 is more difficult to solve. We show via a counter example that the algorithms derived for P1 and others recently published can fail to find a schedulable priority ordering when the gaps are small, even though one exists. We derive an optimal and robust solution to this problem with respect to a simple form of schedulability analysis which assumes the same upper bound on the length of all messages.